Just be smart and you will have a fine time. The areas you are visitng are completely fine.
Now lets eat.
Restaurant Nora (Dupont) is very good, kinda romantic if you can get a seat in the back and not the main dining room. Reservations need to be made well in advance.
DC Coast (14th and K) is my favorite place for the money. A little expensive, but I think well worth it. Sit upstairs, less foot traffic.
New Heights (Conn Ave and ???, near the Woodley park metro) is always nice. Small place and the staff are very nice. Attentive if you want them, leave you alone if you ask.
Cashions Eat Place (Columbia Rd near 18th) is wonderful. Small place with wonderful food. Her fish dishes win awards all the time. I hope Scott is still the bartendar, he's a neat guy.
La Fourchette (18th St and Columbia Rd) is a quaint french Bistro that is very nice. Not terribly romantic, so I would eat there on another evening. The owner is great (and the chef) and his wife is the one who will seat you. Charming in a French kinda way.
What kind of food do you like? I am one of those fish-a-tarians but if you want a good steak and can ask a friend.
www.quikbook.com is a good place to get a break on the high price of hotels in DC. The only hotel I have stayed at in DC was the Hotel Jeffferson and it was very nice. I think it is the Drury Inn at Dupont is the good choice for most affordable.